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This paper focuses on systems of nonlinear second-order stochastic differential equations with multi-scales. The motivation for our study stems from mathematical physics and statistical mechanics, for examples, Langevin dynamics and…
We present a data-driven approach to efficiently approximate nonlinear transient dynamics in solid-state systems. Our proposed machine-learning model combines a dimensionality reduction stage with a nonlinear vector autoregression scheme.…
In a preliminary attempt to address the problem of data scarcity in physics-based machine learning, we introduce a novel methodology for data generation in physics-based simulations. Our motivation is to overcome the limitations posed by…
Diffusive transport of a particle in spatially correlated random energy landscape having exponential density of states has been considered. We exactly calculate the diffusivity in the nondispersive quasi-equilibrium transport regime and…
A space fractional diffusion-like equation is introduced, which embodies the nonlocality in time, represented by the memory kernel and the non-locality in space. A specific example of the nonlocal term is considered in combination with…
In this manuscript, we consider the problem of learning a flow or diffusion-based generative model parametrized by a two-layer auto-encoder, trained with online stochastic gradient descent, on a high-dimensional target density with an…
Solving statistical learning problems often involves nonconvex optimization. Despite the empirical success of nonconvex statistical optimization methods, their global dynamics, especially convergence to the desirable local minima, remain…
Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…
Denoising Diffusion Probabilistic Models (DDPMs) have recently achieved remarkable results in conditional and unconditional image generation. The pre-trained models can be adapted without further training to different downstream tasks, by…
Inspired by many examples in nature, stochastic resetting of random processes has been studied extensively in the past decade. In particular, various models of stochastic particle motion were considered where upon resetting the particle is…
Cloth manipulation is challenging due to its highly complex dynamics, near-infinite degrees of freedom, and frequent self-occlusions, which complicate both state estimation and dynamics modeling. Inspired by recent advances in generative…
For a general class of diffusion processes with multiplicative noise, describing a variety of physical as well as financial phenomena, mostly typical of complex systems, we obtain the analytical solution for the moments at all times. We…
Physics-guided sampling with diffusion priors has recently shown strong performance in solving complex systems of partial differential equations (PDEs) from sparse observations. However, these methods are typically evaluated on benchmark…
We discuss parametric estimation of a degenerate diffusion system from time-discrete observations. The first component of the degenerate diffusion system has a parameter $\theta_1$ in a non-degenerate diffusion coefficient and a parameter…
Data-driven learning approaches for physics simulation, sometimes referred to as world models, have emerged as promising alternatives to traditional physics simulators due to their differentiable nature. Prior work has demonstrated…
We present a generative modeling framework for synthesizing physically feasible two-dimensional incompressible flows under arbitrary obstacle geometries and boundary conditions. Whereas existing diffusion-based flow generators either ignore…
Diffusion processes are a class of stochastic differential equations (SDEs) providing a rich family of expressive models that arise naturally in dynamic modelling tasks. Probabilistic inference and learning under generative models with…
Using statistical physics methods, we study generative diffusion models in the regime where the dimension of space and the number of data are large, and the score function has been trained optimally. Our analysis reveals three distinct…
To sample from an unconditionally trained Denoising Diffusion Probabilistic Model (DDPM), classifier guidance adds conditional information during sampling, but the gradients from classifiers, especially those not trained on noisy images,…
We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…